Question on Infinite

[von Faulkenstein]

Could the infinite small contain the infinite large?

[Tormod]

Would the infinitely stupid contain the infinitely smart?

Here's a good article on Cantor, who basically revolutionized the concept of infinities:
Georg Cantor - Wikipedia, the free encyclopedia

...and an article on actual infinities:
Actual infinity - Wikipedia, the free encyclopedia

[Qfwfq]

Originally Posted by Jet2

Are infinite large and infinite small the same?

Infinitely small is just a loose way of saying infinitesimal.

In calculus, a term is said to be infinitesimal in a given limit if this limit is zero. For the same limit, the reciprocal of the term is infinity. Infinite cardinality is yet another definition; a set has infinite cardinality if and only if a bijection is possible between it and some proper subset of it.

[Jet2]

If the limit of infinitely small is infinity, then does zero ever exist?

Jet2

[von Faulkenstein]

Could one consider the infinite number of transcendental numbers between two fractions--even if these two fractions are extremely close together?

[ughaibu]

This page is pretty good: Peter Suber, "Infinite Sets"

[Jay-qu]

yes - there are just as many numbers between 0-1 as there are between 0-1,000,000,000,000,000

[Pyrotex]

Originally Posted by Jet2

Thanks CraigD!
Just found a book called "The Infinite Book - A short guide to the boundless, timeless and endless". You are right, it's very interesting indeed.

I learned about infinity while in the 10th grade. I found a book: "One, Two Three... Infinity" by George Gamov.

It may be difficult to find now, but that was one wonderful, mind-expanding book.

[Pyrotex]

Originally Posted by Jet2

If the limit of infinitely small is infinity, then does zero ever exist?

Absolutely!!

Zero is the limit of 1/x as x goes to infinity.

[Qfwfq]

However, unlike infinity, zero does not exist only as a limit, it is a number.